# BCE methods

#### Kenneth

##### Not Alot
There are some basic methods around: corners first = CF, edges first = EF (uncommon), block methods (no abbreavation used for blocks) and layer by layer = LBL. Within these basic methods there are a varaity of specific methods like Guimond for CF or Fridrich for LBL.

Now I found there must also be a basic style I named BCE = blocks, corners, edges. A typical BCE method is Roux.

But that's not the only one. You can create a whole family of BCE methods, start from some block(s), solve the rest of the corners and end by doing the edges that are left. I recently posted here about a method I named Petrus - Ortega that is a BCE method. That method I'm currently learning but I modified it a little. Now I'm not doing a full 3x2x2 at start but two opposite 2x2 blocks leaving the M-slice free. then I'm using Ortega step 2+3 for corners. ca 80 cases, I'm at about 60 now =) The ending 8 edges I solve first the two FR/FL and then, for the rest using a style where I pair opposite edges two by two while orienting them and then sort the pairs out (if I get the two FL edges correct while doing this I end in ELL). If I learn all cases for corners and practice the intuitive parts a little more I can solve the cube in less than 45 turns (STM) on average

An other BCE is: start as I do = two 2x2's, orient one more corner on the FL side (U or D colour) and then orient the last five using an alg and then separate layers (Guimond style). For next step sort out FR/FL and FD/BD edges. Orient LL-edges while doing the last FD/BD edge, end in PLL, also a sub 45 turn method.

But as I said above, there is a whole family spanning from easiest beginner to the advanced methods I have described here.

Anyone intressted in BCE methods? I will in the near future try to make a description of at least the Ortega 2+3 (O23) style, maybe also the Guimond approach. Have some more algs for the corners to collect first only.

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##### Member
Kenneth, I would be interested in reading more about your BCE methods. I use a corners first method as my "preferred" (or most comfortable) method, which seems to me so much simpler than the LBL methods, although most of the posters here seem to prefer Fridrich.

##### Member
I'd be interested in seeing other methods and paradigms

#### Kenneth

##### Not Alot
A little start of descriptions is a Link to a SveKub page that has got algs for orienting the five corners of the Guimond approach (the text of the page is in Swedish but the algs works anyway =)

Newer mind the blue arrows, those are if you use this for CF/2x2x2, learning the arrows you can predict separation during inspection. but here we do the corners as the second step so there is no chance you will see them in the inspection (OK, you will of course see the corners, but won't be able to predict the separation in 15 seconds if the blocks are not solved yet or they are wery easy to solve)

When you see the move count for this step you start to understand why this is a nice method =)

For separation you can not use the algs at the page for all cases, only 1 and 4 are valid and there are more cases than those. That because we also like to pair up the two D corners before we place them, but it's wery intuitive so you don't need algs for that, use only R2 + U/U'/U2 turns and it will work fine.

Edit: for the separation case where both D corners are down but swapped it's better to use an alg: R d' L U2 L' d R (the alg also swaps URF-ULB)

To be continued...

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#### pjk

Staff member
I'd definitely be interested. I plan on working on methods like this a lot after I go sub-14 w/ Fridrich.

#### AvGalen

Corners first is pretty easy and intuitive because you do 1 type of piece first (corners) and then the other type (edges).
Layer by layer is also very intuitive and easy because that is just how people normally approach problems (1 step at a time, foundation -> ... -> finish)
Block building is an approach that has a lot of potential, but is less intuitive. That means you need more practice, but I think eventually the benefits will be really great.

I think it is amazing that after all this time, people are still trying to find better ways to solve this puzzle.

#### Kenneth

##### Not Alot
When corners are done the next thing to do is the FR and FL edges (For me the side where the last two D corners goes is the F side not the R side as you might think). There are quite many cases for those: (8*2 = 16) * (7*2=14) = 224 totaly so there's no way I will learn to solve all in one go. But there are some basic algs that are pretty easy to set up for, reducing the number of cases to a few.

Here are some of the most important moves you can use (do the inverse to set up the cases) :

F M2 F' (F M/M' F' is also nice =)

F U2 M/M' U2 F'

F M U M U' F'

And mirrors.

To orient both that are in place use: F M2 U2 M U2 F' (M->M' if you also like to swap them) - to orient only one of them : R U M U2 M2 U R'

(Note that these algs does not preserve FD/BD edges, no LL edges and M-slice centres)

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##### Member
I think it is amazing that after all this time, people are still trying to find better ways to solve this puzzle.

I agree. With most puzzles, once it's solved it's finished - you already know the answer, so what's the point? But the wonderful thing about this puzzle is that there's always something else you can do with it - whether it be making different designs with it or finding a better way to solve it, etc.

#### Kenneth

##### Not Alot
I said it before: I'm more into cubing to create methods than I am trying to get really fast (like to but does not try that hard =)

To me methodising (maybe "methodizing"? I like Oxford spelling =) is the most fun it can get

Next part in the Guimund approach will be: orient last six edges, sort out and place FD/BD (about the same thing as for corners). That will take us to the ending PLL. But I have not got all algs yet so it will wait a day or so...

I start to describe the Guimond style because it is so much easier to learn or try out for most cubers. The only algs you have to learn is the corner orientation, the rest can be done using intuition, the ending PLL step most of you already know. For the Ortega style there are 2 * CLL + ELL to learn, not many have any base at all for that.

BTW, is my Guimond style the first method exept Fridrich that takes the full use of PLL in the end? I do not know any others.

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#### Kenneth

##### Not Alot
Next part in the Guimund approach will be: orient last six edges, sort out and place FD/BD (about the same thing as for corners). That will take us to the ending PLL. But I have not got all algs yet so it will wait a day or so...
OK, I took a look at Roux page to compare my style to his. He is doing almost the same but a bit diffrent. At first there is orientation of all six edges, then Roux places UR-UL edges so he can end in M-permutation, edges + centres. But in my method that way won't solve corner permutation so I do orientation of all six edges, separate and place FD-BD edges + centres and then the PLL.

Algs for orientation : U = U-layer, D = D-layer. 0, 1, 2*, 3 and 4 are number of unoriented edges in each layer. 2* can be 2o = two opposite edges in U-layer and 2a = two adjacent edges in U-layer. for D only 2 is used because there is only the opposite case possible there.

Example: Case U2a-D2 has got two adjacent edges in U-layer and two in D-layer to orient. U0-D2 has got non in U and two in D and so on. If D=1 (D1) then only 1 and 3 are possible for U and if D=0/2 then only 0, 2o, 2a and 4 are possible for U. So if we start by doing an optional U-turn = in cases U2A, U2B, U1 and U3 we get only 9 cases left.

First turn is in 50% of the cases a M or M' = [M] to put either U or D centre on top, then the optional U-turn follows = .

U3-D1 = [M] - - (M' U/U' M/M')
U2a-D2 = [M] - M2 U - (M' U/U' M/M')
U2a-D0 = [M] - M' U M U2 - (M' U/U' M/M')
U1-D1 = [M] - M' U M U - (M' U/U' M/M')
U0-D2 = [M] - M U M U' - (M' U/U' M/M')
U2o-D0 = [M] - M' U M U' - (M' U/U' M/M')
U2o-D2 = [M] - M U2 M U2 - (M' U/U' M/M')
U4-D0 = [M] - M' U2 M U2 - (M' U/U' M/M')
U4-D2 = [M] - M' U M' U2 M' U M U - (M' U/U' M/M')

As you can see all algs ends in the same way = (M' U/U' M/M') That's why it is in a parentesis, putting focus on the important turns. First case U3-D1 is only these turns so that one we solve every time, makeing the end familar in no time. And that's good because for the last two turns you can choose the direction = U or U' and M or M', that way you can start to work on separation of FD/BD edges while ending the alg, it's wery intuitive and should be possible to use by any who tries this method.

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Next thing is to create algs for corner orientation. some of the 2x2x2 algs at Gustav Fredells SveKub page destroys my F2B's so it's needed. After that I can make a summary for this method (I only got a few of the corners cases to go and then I know the full method, it's pretty easy if you alredy know PLL, OK, corner recognition is hell if you are not used to it but udmb j tus kgvb k tyjkdjgjhgjdjgjejjjjjjjjjjjjjjjjjjjjjt

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#### Kenneth

##### Not Alot
The Guimond step, simplified stepping stone variation.

For the Guimond step there are three corners oriented in FL and possibly five to go, one in FL and 1-4 in LL rendering a total of 16 cases. These cases I will come to in a later post...

For the seven cases where all for corners are oriented in FL I think most people uses the Ortega algs, or even OLL/CLL/COLL designed for 3x3x3 to get to FL+LL oriented.

But there are shorter algs:

pi : F2 U F2 l' u2 l
H : F2 U2 (F/F')
S : F2 U' F U' (F/F')
-S: F2 U F' U (F/F')
L : R U2 R' F' U' (F/F')
T : F R U2 R' (F/F')
U : F U2 F U2 (F/F')

Here we can do the same thing as for the edges: choose the direction for the last turn = start the pairing up of the two FD-corners. Exept for the pi-case, if anyone can find an alg for that case that is 6 turns or shorter, ends in a F-turn and do not destroy BD-corners, BR, BL, DR and DL edges?... then I'm happy to see that alg =) =) =) (I have no clue how to get a solver to find algs for cases where orientation is ok in two opposite layers so I'm using my fantasy, imagination, Tarot card set, casting of runes e.t.c. to find algs for these cases =)

BTW: the runes says there are no algs shorter than six turns for the pi case... but I do not always trust them

I think most people prefer to do the algs in R rather than F, I use F because I view the cube as it is the F and U layer corners I solve to minimise cube orientations, when doing the algs I normaly use L, not R =)

Otimisation: If the two FD corners initially are in a pair, if it is the correct pair, then it is a normal CLL-case but it can also be any of the four LL corner pairs, then it's possible to use pseudo CLL and then end in F2 to compleatly solve all the corners. It is also possible to do that if the two corners in the FD pair are swapped. then use pseudo Ortega 2+3 algs... I use it sometimes if I can reconise the cases, I ofthen fail to do that or think it is some diffrent case ending up in a bad permutation ... but it's learnable

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#### Kenneth

##### Not Alot

I just solved in about 25 seconds (don't know exactly, the battery in my timer is out) using the Guimond style algs for corners. Had easy first 2x2, normal second = about 10 turns for both. Easy corners (all seven algs are), had only U F2 for separation and also skiped permutation for LL corners = ca 8 turns. Normal FM-edges = ca 7 turns. Normal last six edges, ca 12 turns and because of the skiped corner permutation it was only a U-PLL in the end = 7 turns. Totaly about 42 turns and no luck.

Honestly, I think this method can be very fast in the easier solves, sometimes I solve a little lucky in less than 35 turns (most often I do around 50, patrly because I do not know all cases, it will get better)

#### Kenneth

##### Not Alot
After all Guimond I put a little Ortega in between. Here are all algs you need to do the corners in two steps (after you initialy put down the last two D-corners of corse =)

OLL :

U : F R U R' U' F'
T : R U R' U F' U' F
L : R U' R' U' F' U F
S : R U R' U R U2 R'
-S : R U2 R' U' R U' R'
H : R2 U2 R U2 R2
Pi : R U Ra' U' Ra U R'

PBL :
( U + D pairs solved: alg )

2 + 1 : T-PLL or : (x) U2 R' U R U2 Ra' U R U' L
1 + 2 : A, J, T PLL works fine
1 + 1 : r2 U' L2 Ua' L2 U' r2 D2
0 + 1 : R d' L U2 L' d R'
0 + 2 : L' U l d R2 D R' U' R D' R2

There is no 0 + 0 perm because the two first corners are always solved. I can use all my Ortega 2x2x2 algs for this step exept for the 2 + 1 perm, A-PLL destroys RD and LD edges. I only had to add double layer turns at some points for the perms and then all worked =)

To use this as a full method, start by doing the two opposite 2x2's, do these Ortega steps, use the FR/FL edges method from the earlier post. Solve six last edges as in the earlier (but not that early as the one abot F-edges) post, end in EPLL (or use Roux for the last six edges, it's almost the same)

Next I think I will take a couple of scrambles and make example solves for the Guimond simplified and Ortega 2-step methods (the stepping stones). Later I will fix the algs for Guimond 5 corner (few to go but I'm not used to do that so I have to learn recognition while searching for algs so it takes some time) and even later the rest of the algs for Ortega 2+3 (collecting but still miss a bunch).

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#### Kenneth

##### Not Alot
This will be the first example solve:

Scramble :
B2 U L F2 D' R' B' U' B2 D B D F' R2 D' R2 D2 R' F L' F' L2 B2 D' F2

Step 1 = F2B :
F2 D : builds two pairs
M' U2 (y) M' U M' U M : insetrs two edges and two centres compleating the blocks

A little lucky getting the two pairs only by reversing the last two turns of the scramble.
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From this start I will continue by first doing the simple Guimond, then Ortega two step and also a optimized solve where I use whatever I got to get it done. (for the first two I will stick to the methods even if I know a better way)
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Step 2 = Guimond corners :
U2 L : orients D
(y') L' U L F U' F : orients U
U F2 U F2 : pair up and place D-corners (separation)

Step 3 = FR/FL edges :
U' M' F M F2 M2 F : pairs up and places both at once

Step 4 = six edge orientation :
U M' U2 M U M U M' U M' : worst case
U2 M2 U M' U2 M : separation, bad case

Step 5 = PLL :
A-PLL (for example : F R' F L2 F' R F L2 F2)

(I also tried this but did a (y2) before step 4 and then I skiped separation, end was a R-PLL, because of the symetry of the case it's probably easy to learn when it is a good idéa to do (y2) first)

Step 1 and 5 was a little easier than the average, step 2 and 3 normal and step 4 terrible. Total number of turns got to 53. When I first created this method I thougth it cuold do sub 45 on average but did not think so much about separation of D pieces. The real average is 48 something I guess, but that's not bad either. Well, the advanced Ortega still holds for sub 45 but I'm not done with it yet so it may change

The Ortega solution using this start will wait until tomorrow...

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#### Kenneth

##### Not Alot
Ok, now Ortega two step, the scramble and first step is the same as for the solve above:

Scramble :
B2 U L F2 D' R' B' U' B2 D B D F' R2 D' R2 D2 R' F L' F' L2 B2 D' F2

Step 1 = F2B :
F2 D : builds two pairs
M' U2 (y) M' U M' U M : insetrs two edges and two centres compleating the blocks

Step 2 = Ortega corners :
(y') F2 U L' U' L : orients D
R U2 R U R' U R (Sune) : orients U + PBL skip!

Step 3 = FR/FL edges :
U F' M U' M U F : set up U and F, put in first edge, put in second edge, restore F

Step 4 = six edges orientation :
M U M' U' M' : orient
U2 M' U2 M' : separate FD/BD

Step 5 = EPLL :
U-PLL (for example R2 d' M' U2 M d' L2)

Because of the PBL skip this vent as a advanced Ortega 2+3 solve (or CLL) ending in a nice 44 turns. Average PBL is like 7 turns if you also count skips so if I had done that too this had been a little over 50 turns, not bad for a method that uses like 25-30 algs (don't know if I shall count FR/FL edges as algs or intuitive, I'm in the middle)

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#### Kenneth

##### Not Alot
Because the previous solve became lucky (or as the advanced Ortega 2+3) I made a new one, placing the last two D-corners a little diffrent got me to a 2-step for corners :

Scramble and first step as before,

Step 2 = Ortega corners :
(y) F2 U' F U2 F' : orient D
U F2 U2 F' U2 F2 : orient U (H-case)
L' B L' F2 L B' L' F2 L2 : PBL (1+2) (eh, what are those LBL's doing there? this is BCE!)

Step 3 = FR/FL edges :
F' M F : pair up and place both, very nice case =)

Step 4 = last six edges :
U' M U M U M' U M : orient
U' M U2 M' : separate FD/BD

Step 5 = EPLL :
U-PLL (for example : L2 d M' U2 M d R2)

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So, now there is a Guimond, a Ortega and a advanced Ortega solve there.

I also tried a PF ("Pairs first" or maybe "columns first", also a BCE method) starting from those pairs I got in the beginning, did two more, CLL (CF algs works if you use DBL layers to preserve the pairs), placed R/L centres and RD/LD eges, end as for the Ortega style presented here. No comments, really optimized (saved turns and looked ahead more than normaly, nearly a FMC), may have errors because I did not check.

Sramble as above :
Solution : F2 D F U' M U F U (y') L' M U B2 R B R' B l M' U2 S M S U S' M2 U M' U2 M U M' U' M2 U M2 U2 M2

37 STM, no luck!

Edit: Kåre Krig found an Error for me in the last solve, y->y' that I now fixed =)

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#### Kenneth

##### Not Alot
Took my first (terrible) average using the Ortega 2+3 (or maybe I shall call it EG? both Erik and Gunnar are two realy great speedcubers I know pretty well so I must honor them a little I think, from now on I refer to it as EG =)

Average : 42.93

Times : 38.75 50.62 49.26 44.09 37.82 43.81 (54.29) 42.74 41.25 (34.55) 43.44 37.52

Best time 34.55 I skiped M-slice centres and FD edge while doing the FR/FL edges. So I solved the BD edge and did ELL.

I think you can see a little progress if you compare the first half by the second, this was the first time I speedsolved more than a few times in a row using this, I think practice for a couple of days can take me to sub 35. Using LBL I do around 30 on average if I am warmed up, here I didn't do that. but I did errors, got cases I don know how to solve and sometimes even can't reconise...

#### Kenneth

##### Not Alot
Ok guys!, the grandmaster BCE:

Step 1 : solve for pairs, put them in any slot = order does not matter
Step 2 : treat it as it is a 2x2x2 with one side oriented and use the full EG method (120 cases*) to reach columns first (use dbl layer turns to preserve the pairs)
Step 3 : compleate F2B = R/L centres and RD/LD edges (short and wery intuitive step)
Step 4 : as last six edges + EPLL or Roux last step (about the same stuff)

* for the cases where two pairs is diagonally swapped, then end the last pair like, if last turn is R then do R' F2 R2 instead and you swap the pairs before CLL and get rid of 40 cases =) (if last is R2 then you do F2 R2 instead, only one extra turn to solve F2L permutation!)

Edit: darn!, some of my shortest EG algs breaks the pairs no matter how I do But there are others, slightly longer that I can use instead. I'm already pretty sure this will be my method for the future, it's so easy to solve a cube like this if you know EG (I'm learning, again, two years ago I knew them all), just did a 22.17 solve, one of the better non lucky solves I ever did =) But mostly I'm slow because of look ahead (look ahead = LAH, or is there a TLA for that already?), it's always slow when learning and I always sucked in LAH anyway.

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